几类图弱控制的广义束缚数

The general bondage number of weak bomination for some graphs

对任一图G,其弱控制的广义束缚数定义为:b′w(G)=min{t| F E(G),如果|F|=t,则有γw(G-F)>γw(G)}.本文给出了几类图弱控制的广义束缚数的精确值.称b′w(G)=1图为弱控制去边临界图,简记为γw-ER-critical,本文研究了正则图是弱控制去边临界图的充要条件,以及一般图的必要条件.

For any graph G, the general bondage number of γ\-w, b′\-w(G) is defined to be the minimum cardinality of every arbitrary set of edges whose removal from G results in graph G′ satisfying γ\-w(G′)>γ\-w(G). We give exact values of b′\-w(G) for some classes of graphs. And we consider the special case of b′\-w(G), that b′\-w(G) is equal to 1, we call G is edge-removal-critical(ER-critical). Then give necessary and sufficient condition for regular graphs to be γ\-w-ER-critical and necessary condition for general graph to be γ\-w-ER-critical.